The Energy to Momentum Calculator helps determine the momentum of an object or particle based on its energy. It supports both classical mechanics and relativistic physics, depending on the speed and mass of the object. This tool is widely used in particle physics, space science, and mechanical engineering. It allows users to analyze motion in systems where energy and mass interplay under Newtonian or Einsteinian laws. This calculator is part of the Momentum and Energy Conversion Calculator category.
By linking energy and momentum, users gain insights into object behavior at different velocity scales—from slow-moving mechanical objects to particles traveling near the speed of light.
Formula of Energy To Momentum Calculator
There are three main equations used depending on the context:
1. For Non-Relativistic Speeds (v much less than c):
p = √(2 × m × E)
Where:
- p = momentum (kg·m/s)
- m = mass of the object (kg)
- E = kinetic energy (J)
This formula assumes classical mechanics and is valid only when the object’s speed is significantly less than the speed of light.
2. For Relativistic Particles (massless or near-light-speed motion):
p = E / c
Where:
- E = total energy (J)
- c = speed of light = 299,792,458 m/s
Used for photons or very high-speed particles, such as those in particle accelerators.
3. General Relativistic Formula (for objects with rest mass at high velocity):
p = √(E² − (m × c²)²) / c
Where:
- E = total energy (J)
- m = rest mass (kg)
- c = speed of light (m/s)
This is a comprehensive formula that accounts for both energy and rest mass and is valid across all speed ranges.
Quick Reference Table
Here’s a table to help interpret momentum values from different energy inputs under simplified assumptions. These are helpful for checking quick estimates:
| Type of Calculation | Energy (J) | Mass (kg) | Momentum (kg·m/s) |
|---|---|---|---|
| Non-Relativistic | 50 | 2 | 14.14 |
| Non-Relativistic | 100 | 5 | 31.62 |
| Relativistic Photon | 3 × 10⁻¹⁹ | 0 | 1 × 10⁻²⁷ |
| High-Energy Particle | 1 × 10⁻¹⁰ | 9.11 × 10⁻³¹ | ≈3.33 × 10⁻²² |
Note: For relativistic cases, extremely small or large values highlight the scale involved in high-energy physics.
Example of Energy To Momentum Calculator
Case 1: Non-Relativistic Object
You have a 4 kg object with 200 J of kinetic energy.
Step 1:
Use the formula:
p = √(2 × m × E) = √(2 × 4 × 200) = √1600 = 40 kg·m/s
So, the momentum is 40 kg·m/s.
Case 2: Photon with Energy
Energy of a photon is 3 × 10⁻¹⁹ J.
Step 1:
Use the formula:
p = E / c = 3 × 10⁻¹⁹ / 299,792,458 ≈ 1 × 10⁻²⁷ kg·m/s
This result shows the very small momentum carried by a single photon.
Most Common FAQs
Yes. For slow-moving objects, use the classical formula. For photons or high-speed particles, use the relativistic equations.
Because momentum behaves differently under Newtonian and relativistic physics. The classical formula assumes low speeds, while the others account for relativistic effects at high speeds or for massless particles.
Momentum helps describe motion, collisions, and force interactions. It is conserved in isolated systems, making it fundamental in mechanics, astrophysics, and particle physics.